Orthogonal Frequency-Division Multiplexing (OFDM), also referred to as “multi-carrier modulation” (MCM) or “discrete multi-tone modulation” (DMTM), splits up and encodes high-speed incoming serial data, modulating it over a plurality of different carrier frequencies (called “subcarriers”) within a communication channel to transmit the data from one user to another. The serial information is broken up into a plurality of sub-signals that are transmitted simultaneously over the subcarriers in parallel.
By spacing the subcarrier frequencies at intervals of the frequency of the symbols to transmit, the peak power component of each modulated subcarrier lines up exactly with zero power components of the other modulated subcarriers, thereby providing orthogonality (independence and separability) of the individual subcarriers. This allows a good spectral efficiency (close to optimal) and minimal inter-channel interference (ICI), i.e. interferences between the subcarriers.
For these reasons, OFDM is used in many applications. Many digital transmission systems have adopted OFDM as the modulation technique such as digital video broadcasting terrestrial TV (DVB-T), digital audio broadcasting (DAB), terrestrial integrated services digital broadcasting (ISDB-T), digital subscriber line (xDSL), WLAN systems, e.g. based on the IEEE 802.11, cable TV systems, etc.
However, the advantage of the OFDM can be useful only when the orthogonality is maintained. In case the orthogonality is not sufficiently warranted by any means, its performance may be degraded due to inter-symbol interference (ISI) and inter-carrier interference (ICI).
This could happen as a result of synchronization issues between the clocks of the emitter and of the receiver within the OFDM system. These issues comprise:                Symbol Timing Offset (STO) and,        Carrier Frequency Offset (CFO)        
Carrier Frequency Offset is notably caused by the mismatch of the oscillators of the emitter and of the receiver of the OFDM system, the nonlinear characteristic of the wireless channel and the Doppler shift when the emitter and/or the receiver are moving.
Even small frequency offsets can cause large signal to noise ratio (SNR) and bit-error-rate (BER) degradation. In particular, OFDM systems employing time-domain differential demodulation are very sensitive to the CFO.
Therefore, an accurate CFO estimation and correction algorithms should be employed to avoid performance degradation.
Several solutions have been proposed so far but they are not entirely satisfactory and efficient. These solutions have one or several of the following drawbacks:                Some techniques decrease the spectral efficiency by using dedicated transmitted data or sample sequences to train the CFO estimator at receiver's side. It is the case of many solutions based on pilot signals as for instance described in “Frequency Synchronization Algorithms for OFDM systems suitable for Communication over Frequency Selective Fading Channels” of Ferdinand Classen and Heinrich Meyr, In Proceedings of the Vehicular Technology Conference (VTC'97).        Some techniques are not accurate enough.        Some techniques require complex implementation.        Some technique implies analog treatment, leading to important silicon overhead.        Some techniques are not fully compliant with OFDM standards (like WLAN, LTE . . . )        
There is thus a need for a solution permitting to improve the situation by providing a better estimation of the CFO.